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Interacting Slow and Fast Dynamics in Precise Spiking-Bursting Neurons [chapter]

Fabiano Baroni, Joaquin J. Torres, Pablo Varona
2005 Lecture Notes in Computer Science  
We have explored the role of the interaction of slow and fast intracellular dynamics in generating precise spiking-bursting activity in a model of the heartbeat central pattern generator of the leech.  ...  These neural signatures are cell-specific interspike intervals in the spiking-bursting activity of each neuron.  ...  Calcium dynamics is often considered to affect mainly the slow depolarization waves. However, the interaction of fast and slow dynamics gives rise to phenomena on both time scales.  ... 
doi:10.1007/11499220_11 fatcat:snwety37rvgjtocbvuq6blmgxa

Detection of Activation Sequences in Spiking-Bursting Neurons by means of the Recognition of Intraburst Neural Signatures

José Luis Carrillo-Medina, Roberto Latorre
2018 Scientific Reports  
This characteristic neural signature coexists with the information encoded in other aspects of the spiking-bursting signals, and its functional meaning is still unknown.  ...  Experimental findings have revealed the presence of precise cell-type-specific intraburst firing patterns in the activity of some bursting neurons.  ...  Only in recent years the role of fast dynamics in bursting neurons is receiving some attention.  ... 
doi:10.1038/s41598-018-34757-1 pmid:30425274 pmcid:PMC6233224 fatcat:6losaumoufg65aqqdz5bs3uol4

Origin and role of neural signatures in bursting neurons

Roberto Latorre, Francisco B. Rodríguez, Pablo Varona
2007 AIP Conference Proceedings  
These signatures consist of cell-specific spike timings in the bursting activity of the neurons.  ...  Multiple codes can be used to discriminate or contextualize certain inputs, even in single neurons. Dynamical mechanisms can add to the existing hard-wired connectivity for this task.  ...  ACKNOWLEDGMENTS This work was supported by Fundacion BBVA, MEC BFU2006-07902/BFI and MEC TIN2004-04363-C03-03.  ... 
doi:10.1063/1.2709585 fatcat:xhfyxsbfrzazngumr6rzwgskzu

Transitions to Synchrony in Coupled Bursting Neurons

Mukeshwar Dhamala, Viktor K. Jirsa, Mingzhou Ding
2004 Physical Review Letters  
Certain cells in the brain, for example, thalamic neurons during sleep, show spike-burst activity.  ...  We study such spike-burst neural activity and the transitions to a synchronized state using a model of coupled bursting neurons.  ...  states, one associated with burst (slow time-scale dynamics) and the other with spikes (fast time-scale dynamics).  ... 
doi:10.1103/physrevlett.92.028101 pmid:14753970 fatcat:kuqr7kmm2raflixrv2wwwy2nqa

Development of dynamics and synchronization model for coupled neurons using Hindmarsh-Rose model

M. Mamat, P. W. Kurniawan, A. Kartono
2013 Applied Mathematical Sciences  
This paper presents development of dynamics and synchronization of coupled neurons using the Hindmarsh-Rose neuron model.  ...  By this method, we can analyze different pattern of synchronization of two systems by giving delayed-times in fast variable and different time-scales in slow variable.  ...  Phase synchronies appear in slow dynamic at adaptation current variable, chaotic spiking-bursting turn up both neurons.  ... 
doi:10.12988/ams.2013.13012 fatcat:yfasl3gakzcoda5x5a4nie27ly

Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection

John Rinzel, Gemma Huguet
2013 Communications on Pure and Applied Mathematics  
We discuss the mathematical dissection of bursting oscillations using fast/slow analysis and demonstrate the approach using single-cell and mean-field network models.  ...  We review some widely studied models and firing dynamics for neuronal systems, both at the single cell and network level, and dynamical systems techniques to study them.  ...  GH was supported by the Swartz Foundation and in part by the MCyT/FEDER Grants MTM2009-06973, MTM2012-31714, and 2009SGR-859. Bibliography  ... 
doi:10.1002/cpa.21469 pmid:25392560 pmcid:PMC4225813 fatcat:kvokfhpcqnhkrh3d7y4oh2y4cu

Versatile biologically inspired electronic neuron

Jacobo D. Sitt, J. Aliaga
2007 Physical Review E  
Reliability and precision of spike timing is induced in the three channel circuit by injecting noise in the control variable of the slow channel that provides a negative feedback.  ...  The dynamical behavior of this system is studied, showing for the two channel circuit either class-I or class-II excitability and for the three channel circuit bursting and spike frequency adaptation.  ...  Typically, bursting appears due to the interaction of fast currents ͑responsible for the spiking͒ and slow currents ͑responsible for the modulation of that spiking͒.  ... 
doi:10.1103/physreve.76.051919 pmid:18233699 fatcat:htaepuhxpjaijeigoavnohxr6u

Autonomous Bursting in a Homoclinic System

R. Meucci, A. Di Garbo, E. Allaria, F. T. Arecchi
2002 Physical Review Letters  
The phenomen here presented display qualitative analogies with bursting phenomena in neurons.  ...  A continuous train of irregularly spaced spikes, peculiar of homoclinic chaos, transforms into clusters of regularly spaced spikes, with quiescent periods in between (bursting regime), by feeding back  ...  Bursting arises as the slow variables switch the fast ones between steady state and oscillatory dynamics.  ... 
doi:10.1103/physrevlett.88.144101 pmid:11955151 fatcat:l3xnddskxbghng3qq273clxnvi

The effects of synaptic time delay on motifs of chemically coupled Rulkov model neurons

Igor Franović, Vladimir Miljković
2011 Communications in nonlinear science & numerical simulation  
For the inhibitory and excitatory synapses, the system dynamics is determined by the synaptic weight g c , synaptic gain parameter k, time delay s and the external excitation r.  ...  Given the importance of the network motifs, we consider a pair of Rulkov chaotic map neurons, reciprocally coupled via symmetrical chemical synapses with the time delay s.  ...  Acknowledgement This research was performed as part of the work within Project No. 141020, funded by the Serbian Ministry of Science and Technological Development.  ... 
doi:10.1016/j.cnsns.2010.05.007 fatcat:zo7nyn23xzdhlhhyxyozker6qm

Page 1533 of The Journal of Neuroscience Vol. 23, Issue 4 [page]

2003 The Journal of Neuroscience  
Erisir A, Lau D, Rudy B, Leonard CS (1999) Function of specific K ~ chan- nels in sustained high-frequency firing of fast-spiking neocortical inter- neurons. J Neurophysiol 82:2476—2489.  ...  This recovery function regular- ized spike output, which had the important effect of increasing response precision and the information transfer rate.  ... 

Neural Coding With Bursts—Current State and Future Perspectives

Fleur Zeldenrust, Wytse J. Wadman, Bernhard Englitz
2018 Frontiers in Computational Neuroscience  
a slow bursting to a fast spiking regime.  ...  (B) Classification of a subset of all somatic slow-fast (fast subsystem: spiking mechanism, here two-dimensional, slow subsystem: the system that makes the neuron transition between spiking and quiescence  ... 
doi:10.3389/fncom.2018.00048 pmid:30034330 pmcid:PMC6043860 fatcat:jiqxza2sunelfbvfopp53he7v4

A Codimension-2 Bifurcation Controlling Endogenous Bursting Activity and Pulse-Triggered Responses of a Neuron Model

William H. Barnett, Gennady S. Cymbalyuk, Thomas Wennekers
2014 PLoS ONE  
The dynamics of individual neurons are crucial for producing functional activity in neuronal networks.  ...  The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst.  ...  To account for this mutual interaction and to formalize the progression of the burst towards termination, we used slow-fast decomposition.  ... 
doi:10.1371/journal.pone.0085451 pmid:24497927 pmcid:PMC3908860 fatcat:ehzrjtidcnbzvcmdciuveq4zsq

Fast reciprocal inhibition can synchronize bursting neurons

Sajiya Jalil, Igor Belykh, Andrey Shilnikov
2010 Physical Review E  
Through stability analysis, we reveal the emergent mechanism of in-phase synchronization and discuss its implications for various types of bursting neurons and networks.  ...  We study a pair of endogenously bursting neurons with fast nondelayed inhibitory connections.  ...  More precisely, it was shown that stable synchronous oscillations are not possible in reciprocally coupled networks of fast inhibitory spiking cells ͓10,11͔, unless each spiking cell has at least two slow  ... 
doi:10.1103/physreve.81.045201 pmid:20481777 fatcat:5q2sci5dkzbntlz7bygap4xueq

Inhibitory Synchronization of Bursting in Biological Neurons: Dependence on Synaptic Time Constant

Robert C. Elson, Allen I. Selverston, Henry D. I. Abarbanel, Mikhail I. Rabinovich
2002 Journal of Neurophysiology  
With natural synaptic interactions blocked (but modulatory inputs retained), these neurons generated independent, repetitive bursts of spikes with cycle period durations of ϳ1 s.  ...  During the in-phase bursting, the higher-frequency spiking activity was not synchronized.  ...  In bursting neurons, such as those of the pyloric circuit, V pre undergoes slow oscillations crowned by bursts of fast spikes.  ... 
doi:10.1152/jn.2002.88.3.1166 pmid:12205138 fatcat:eympbpj3xfd6hi7m5i3esx2ove

Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons

Justin R. Dunmyre, Christopher A. Del Negro, Jonathan E. Rubin
2011 Journal of Computational Neuroscience  
slow-fast decomposition.  ...  The persistent sodium (NaP) current is observed in every preBötC neuron, and significant modeling effort has characterized its contribution to square-wave bursting in the preBötC.  ...  Acknowledgements We thank John Hayes for assistance in collecting experimental data.  ... 
doi:10.1007/s10827-010-0311-y pmid:21234794 pmcid:PMC3370680 fatcat:te37pytb3jd5pce5uflv7gbic4
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